A probabilistic proof of a formula for Jacobi polynomials by L. Carlitz
- 1 July 1968
- journal article
- Published by Cambridge University Press (CUP) in Mathematical Proceedings of the Cambridge Philosophical Society
- Vol. 64 (3) , 695-698
- https://doi.org/10.1017/s0305004100043383
Abstract
Letbe the Jacobi polynomial as defined by Szegö in (7) (see equation (4) below.) Carlitz in (2) presented among others the following formula Although, as Carlitz claims, this formula may be derived directly from the definition of Jacobi polynomials, a probabilistic proof such as presented below may shed some new light on formula (1), as well as suggest probabilistic proofs for other similar formulas of Jacobi polynomials, e.g. those given by Manocha and Sharma in (4) and (5) and by Manocha in (3). In addition, it is quite possible that this method of proof will result in the derivation of some new formulas for Jacobi polynomials.Keywords
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